a person stands in the center of a frozen pond wearing ice skates. his total weight including his skates is 400 n. he pushes on of his 20 n skates forward at 10 m/s. what is his velocity?

Answer 1

You can't solve this with conservation of momentum, as his leg is attached to his body, and if his body has momentum, the leg moves with the body, and the skates move with the leg.

Now if his skate is detached, and then moved one direction and let go, then
momentum coservation can be used.

skatemass*skate velocity+personmass*personvelocty=0

20*10+(400-20)Vman=0
solve for Vman. Notice it is negative, meaning the opposite direction of the skate.